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On Ackermann's set theory1

Published online by Cambridge University Press:  12 March 2014

Azriel Lévy
Azriel Lévy*
Affiliation:
Massachusetts Institute of Technology, Cambridge and Hebrew University, Jerusalem
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Extract

Ackermann introduced in [1] a system of axiomatic set theory. The quantifiers of this set theory range over a universe of objects which we call classes. Among the classes we distinguish the sets. Here we shall show that, in some sense, all the theorems of Ackermann's set theory can be proved in Zermelo-Fraenkel's set theory. We shall also show that, on the other hand, it is possible to prove in Ackermann's set theory very strong theorems of the Zermelo-Fraenkel set theory.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 24 , Issue 2 , June 1959 , pp. 154 - 166
Copyright
Copyright © Association for Symbolic Logic 1959

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Footnotes

1

The ideas on which this paper is based are contained in the author's Ph.D. thesis submitted to the Hebrew University. The author wishes to express his gratitude to Prof. A. A. Fraenkel and Prof. A. Robinson for their guidance and kind encouragement. This paper was written while the author was a Sloan Fellow of the School for Advanced Study at the Massachusetts Institute of Technology.

References

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